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Hankel loop integral

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1: 5.9 Integral Representations
Hankel’s Loop Integral
See accompanying text
Figure 5.9.1: t -plane. Contour for Hankel’s loop integral. Magnify
2: 10.9 Integral Representations
Mehler–Sonine and Related Integrals
Schläfli–Sommerfeld Integrals
Hankel’s Integrals
In (10.9.20) and (10.9.21) the integration paths are simple loop contours not enclosing t = - 1 . …
§10.9(iv) Compendia
3: 25.11 Hurwitz Zeta Function
§25.11(vii) Integral Representations
25.11.30 ζ ( s , a ) = Γ ( 1 - s ) 2 π i - ( 0 + ) e a z z s - 1 1 - e z d z , s 1 , a > 0 ,
where the integration contour is a loop around the negative real axis as described for (25.5.20).
§25.11(viii) Further Integral Representations
§25.11(ix) Integrals
4: Bibliography C
  • L. G. Cabral-Rosetti and M. A. Sanchis-Lozano (2000) Generalized hypergeometric functions and the evaluation of scalar one-loop integrals in Feynman diagrams. J. Comput. Appl. Math. 115 (1-2), pp. 93–99.
  • J. B. Campbell (1984) Determination of ν -zeros of Hankel functions. Comput. Phys. Comm. 32 (3), pp. 333–339.
  • R. G. Campos (1995) A quadrature formula for the Hankel transform. Numer. Algorithms 9 (2), pp. 343–354.
  • N. B. Christensen (1990) Optimized fast Hankel transform filters. Geophysical Prospecting 38 (5), pp. 545–568.
  • P. Cornille (1972) Computation of Hankel transforms. SIAM Rev. 14 (2), pp. 278–285.
  • 5: 13.10 Integrals
    §13.10 Integrals
    Loop Integrals
    §13.10(v) Hankel Transforms
    For additional Hankel transforms and also other Bessel transforms see Erdélyi et al. (1954b, §8.18) and Oberhettinger (1972, §§1.16 and 3.4.42–46, 4.4.45–47, 5.94–97). …
    6: 13.4 Integral Representations
    §13.4 Integral Representations
    §13.4(ii) Contour Integrals
    §13.4(iii) Mellin–Barnes Integrals